Question: Express your answer as a mixed number simplified to lowest terms. $10\dfrac{1}{5}-5\dfrac{6}{10} = {?}$
Answer: Simplify each fraction. $= {10\dfrac{1}{5}} - {5\dfrac{3}{5}}$ Find a common denominator for the fractions: $= {10\dfrac{1}{5}}-{5\dfrac{3}{5}}$ Convert ${10\dfrac{1}{5}}$ to ${9 + \dfrac{5}{5} + \dfrac{1}{5}}$ So the problem becomes: ${9\dfrac{6}{5}}-{5\dfrac{3}{5}}$ Separate the whole numbers from the fractional parts: $= {9} + {\dfrac{6}{5}} - {5} - {\dfrac{3}{5}}$ Bring the whole numbers together and the fractions together: $= {9} - {5} + {\dfrac{6}{5}} - {\dfrac{3}{5}}$ Subtract the whole numbers: $=4 + {\dfrac{6}{5}} - {\dfrac{3}{5}}$ Subtract the fractions: $= 4+\dfrac{3}{5}$ Combine the whole and fractional parts into a mixed number: $= 4\dfrac{3}{5}$